Crypto SD Revision Question and Answers
Is the exam going to be multiple choice or essay?
The exam will involve problem solving and essays type questions. There will NOT be any multiple choice questions.
You will have to answer all questions.
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Are the exams based on the lecture slides only?
The exams are based on the material presented during the course, which includes lecture slides, recorded lectures and interactive lectures.
Are Past Papers Helpful?
Last year’s paper is most helpful because it was answered remotely, just like this year.
The papers from years before then are a bit helpful, but remember that they were designed for students answering them in a traditional exam hall. Discount questions that can be answered just by looking up the course materials since they would be too easy under this year’s exam conditions.
Euler’s Theorem : Why must gcd(P,n) = 1?
Proof that decryption undoes encryption relies on Pφ(n) % n = 1. This is a version of Euler’s theorem, which is only true if gcd(P,n) = 1. This is just a property of the underlying mathematics. If it is not true then encryption followed by decryption will produce a different number than the one we started with. P is the plain text.
RSA : How are Prime Numbers p and q chosen?
The length of n (the number of bits) is chosen based on international standards.
Each prime has half the number of bits.
A random number with this number of bits – 2 is chosen with a secure random number generator. The bits 11 are added in the least significant bit positions. This generates an odd number where p % 4 = 3.
This number is tested to see if it is a prime. If not, then 4 is added and the test repeated until a prime is found.
This process is repeated for the second prime.
This is not an Enigma machine. This is an open ended question to test your understanding of rotor machines. Half marks are earned by a general description of how rotor machines work. More marks are obtained by also noticing that a Caesar
cipher is not very good for a rotor machine because the substitution is always the same no matter what position the rotor is in. The final mark is obtained by noticing that 3+15+7+4 = 29, the number of letters on the rotor. So the cipher text is always the same as the plain text.
What does R=4.7 in English Mean?
There are 26 letters in the English alphabet. If each is equally likely to occur then the entropy formula gives log2(26) = 4.7.
How is r Calculated?
r is the entropy per letter based on actual frequencies of letters in the English language. It is found experimentally and depends on the size of text segment, ie N. If N = 1 it is just the single letter frequency, if N = 2 it the frequency of all letter pairs, and so on. Spaces are not normally included. As N increases, the value of rN/N tends to the same value, which is the overall value of r.
What is a Multiplication Table?
Think of multiplication tables in primary school. You memorise the answers to 3×4,7x8andsoon. Alltheanswersfordigits1to9arewritteninatable.
Cryptography uses different rules for multiplication: multiplication with integers mod n; multiplication with polynomials mod an irreducible polynomial, but the idea is the same. The aim is to create a table that can be memorised, but this time memorised by a computer (stored in the computer memory).
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